On primitive factorizations for n-D polynomial matrices

In the study of the analysis, synthesis and realization of multivariate networks, n-dimensional (n-D) systems stability theory and feedback control, and n-D signal processing, it is often necessary to consider the feasibility of a factorization for a given n-D polynomial matrix A(z) in the form A₁(z) A₂(z), where A₁(z ) and AA₂(z) are n-D polynomial matrices. The author reports on one such factorizations, i.e., the primitive factorization. A criterion for the existence of primitive factorizations for a class of n-D polynomial matrices is presented. The criterion can be used to construct a primitive factorization, when it exists, for an n-D polynomial matrix in this class